Abstract: Following the prediction and confirmation that interstitial hydrogen forms shallow donors in zinc oxide, inducing electronic conductivity, the question arises as to whether it could do so in other oxides, not least in those under consideration as thin-film insulators or high-permittivity gate dielectrics. We have screened a wide selection of binary oxides for this behaviour, therefore, using muonium as an accessible experimental model for hydrogen. New examples of the shallow-donor states that are required for n-type doping are inferred from hyperfine broadening or splitting of the muon spin rotation spectra. Electron effective masses are estimated (for several materials where they are not previously reported) although polaronic rather than hydrogenic models appear in some cases to be appropriate. Deep states are characterized by hyperfine decoupling methods, with new examples found of the neutral interstitial atom even in materials where hydrogen is predicted to have negative-U character, as well as a highly anisotropic deep-donor state assigned to a muonium-vacancy complex. Comprehensive data on the thermal stability of the various neutral states are given, with effective ionization temperatures ranging from 10 K for the shallow to over 1000 K for the deep states, and corresponding activation energies between tens of meV and several eV. A striking feature of the systematics, rationalized in a new model, is the preponderance of shallow states in materials with band-gaps less below 5 eV, atomic states above 7 eV, and their coexistence in the intervening threshold range, 5-7 eV.